Problem: $80$ people attended a baseball game. Everyone there was a fan of either the home team or the away team. The number of home team fans was $34$ less than $2$ times the number of away team fans. How many home team and away team fans attended the game?
Answer: Let $x$ equal the number of home team fans and $y$ equal the number of away team fans. The system of equations is then: ${x+y = 80}$ ${x = 2y-34}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${2y-34}$ for $x$ in the first equation. ${(2y-34)}{+ y = 80}$ Simplify and solve for $y$ $ 2y-34 + y = 80 $ $ 3y-34 = 80 $ $ 3y = 114 $ $ y = \dfrac{114}{3} $ ${y = 38}$ Now that you know ${y = 38}$ , plug it back into ${x = 2y-34}$ to find $x$ ${x = 2}{(38)}{ - 34}$ $x = 76 - 34$ ${x = 42}$ You can also plug ${y = 38}$ into ${x+y = 80}$ and get the same answer for $x$ ${x + }{(38)}{= 80}$ ${x = 42}$ There were $42$ home team fans and $38$ away team fans.